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arXiv · 1711.06316

Knot contact homology and open Gromov-Witten theory

Tobias Ekholm
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Abstract

Knot contact homology studies symplectic and contact geometric properties of conormals of knots in 3-manifolds using holomorphic curve techniques. It has connections to both mathematical and physical theories. On the mathematical side, we review the theory, show that it gives a complete knot invariant, and discuss its connections to Fukaya categories, string topology, and micro-local sheaves. On the physical side, we describe the connection between the augmentation variety of knot contact homology and Gromov-Witten disk potentials, and discuss the corresponding higher genus relation that quantizes the augmentation variety.

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Tobias Ekholm. 2017-11-16. Knot contact homology and open Gromov-Witten theory. https://arxiv.org/abs/1711.06316

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